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On a Multigrid Method for Tempered Fractional Diffusion Equations
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DOI：10.3390/fractalfract5040145.png)
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In this paper, we develop a suitable multigrid iterative solution method for the numerical solution of second- and third-order discrete schemes for the tempered fractional diffusion equation. Our discretizations will be based on tempered weighted and shifted Grunwald difference (tempered-WSGD) operators in space and the Crank-Nicolson scheme in time. We will prove, and show numerically, that a classical multigrid method, based on direct coarse grid discretization and weighted Jacobi relaxation, performs highly satisfactory for this type of equation. We also employ the multigrid method to solve the second- and third-order discrete schemes for the tempered fractional Black-Scholes equation. Some numerical experiments are carried out to confirm accuracy and effectiveness of the proposed method.
Keyword:
high-order tempered-WSGD operator
the tempered fractional derivative
multigrid method
damped Jacobi method
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3.3
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4.3K
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HIGH ORDER ALGORITHMS FOR THE FRACTIONAL SUBSTANTIAL DIFFUSION EQUATION WITH TRUNCATED LEVY FLIGHTS具有截断LEVY飞行的分数阶实质扩散方程的高阶算法
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